相关论文: On Randomness in Quantum Mechanics
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography,…
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of motion…
A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
In Quantum Physics there are circumstances where the direct measurement of particular observables encounters diffculties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable…